Question

The number of bottles of whiskey that a store will sell in a month at a price of p dollars per bottle is . N(p) = (2250)/(p+3) Find the rate of change of this quantity when the price is $7.

Answer 1

Answer: The rate of change of this quantity would be -22.50.

Explanation:

Since we have given that

the number of bottles of whiskey that a store will sell in a month at a price of p is given by

`N(p)=(2250)/(p+3)`

We need to find the rate of change of this quantity:

So, we will find the first derivative with respect to p.

`N'(p)=2250(-1)(p+3)^(-2)`

if p = 7 , then the rate of change becomes,

`N'(7)=-2250(7+3)^(-2)=(-2250)/(10^2)=(-2250)/(100)=-22.50`

Hence, the rate of change of this quantity would be -22.50.